Impossible Cryptarithm

Computer Science Level 4

$\begin{array}{ccccc} & A & B & C & D\\ \times & & & & E\\ \hline & F & G & H & I \end{array}$

Given that $A, B, C, D, E, F, G, H, I$ are distinct non-zero digits, find $A+E+H+I$ .

The answer is 12.

5 solutions

Juan Mtz
Jun 23, 2015

Using R, is not the optimal but apparently it works.

Can't we do this problem without programming? 😅

Prem Chebrolu - 2 years, 7 months ago

Rajat De
Jun 23, 2015

Moderator note:

Note, you can enter code directly using the backtick tags, i.e. open with ```cpp and close with ``` .

Daniel Liu
Jun 21, 2015

A computer program will give $4\times 1738 = 6952$ $4\times 1963 = 7852$ as the only solutions. Note that in either of these solutions, $A+E+H+I=\boxed{12}$ so we are done.

Mathematical solution plzz..

Ashish Tomer - 5 years, 11 months ago

That isn't a mathematical solution. Please post a solution that uses mathematics to derive the solution.

Tanish Islam - 5 years, 11 months ago

I'm disappointed in these "Solutions" ... I thought you guys were supposed to be geniuses

Alex Li - 5 years, 11 months ago

Look at the other posts for actual solutions. This was really meant to only be a placeholder.

Also, please do not comment with a demeaning tone, it is disrespectful.

Daniel Liu - 5 years, 11 months ago

I do it by hand and I find also $3458\times2=7916$ , and it gives the same answer. Can you give me more detail about your computer program, please?

Mountassir Farid - 5 years, 11 months ago

3458*2=6916 hence solution looks incorrect

Shambhu Singh - 5 years, 11 months ago

Yes, you are right! In fact, I worked on $3548\times2=7096$ , and this give me the answer $20$ which is not accepted. So, I switch $4$ and $5$ and forget to update the last digit in the result. By chance, I get the correct answer!

Mountassir Farid - 5 years, 11 months ago

@Mountassir Farid – 0 isn't positive

Ram Yeshwanth M - 5 years, 11 months ago

F G H I are distinct ....in your case F and I are same i.e. equal to 1

Abhishek Bhardwaj - 5 years, 11 months ago

Nathan Sproul
Jun 24, 2015

I have to use Excel a lot at work, so I like to do my CS solutions in Excel when I can to practice my VBA. This was my solution:

I know, not the most elegant :p

Nathan Sproul - 5 years, 11 months ago

What is the easiest way to construct a permutation in excel? This would avoid you having to do the check if "if a = b or ....".

Calvin Lin Staff - 5 years, 10 months ago

Jesse Nieminen
Jun 26, 2019

from itertools import permutations

for (A, B, C, D, E, F, G, H, I) in permutations("123456789"):
    if int(A + B + C + D) * int(E) == int(F + G + H + I):
        print(int(A) + int(E) + int(H) + int(I))

1
2

12
12

Impossible Cryptarithm

The answer is 12.

5 solutions

Moderator note:

0 pending reports